The sedimentation coefficient

Let us start with a semi-dilute solution where each monomer is subjected 

To achieve this, we consider one monomer, M, that feels the flow fields from all neighboring monomers, M. This approach is due to Kiiitwood and Risemarm J. Chem. Phys. 16,565 (1948)] and is illustrated in Fig. Vn.2. The velocity at M is a sum of backflow contributions from all sources of force  

One monomer, M , is subjected to a force f. It then moves in the solvent and creates a backflow indicated by the arrows. A second mmomer, M, then drifts in this flow field. 

Subtraction of the second term arises from the following. To maintain the solvent in the steady state, we must have a pressure gradient Vp which exactly balances the average force if = cf ono per cm ) 

The second term in eq. (VII.4) corresponds to the effect of this average pressure gradient. If we compute the average velocity, we must weight the probability of finding monomers at M and M by the correlation function (c (0) c (r))/c. Thus, we arrive at 

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At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

The stationary-state velocity per unit acceleration is a parameter which characterizes the settling particle and is called the sedimentation coefficient s ... 

In a solution of molecules of uniform molecular weight, all particles settle with the same value of v. If diffusion is ignored, a sharp boundary forms between the top portion of the cell, which has been swept free of solute, and the bottom, which still contains solute. Figure 9.13a shows schematically how the concentration profile varies with time under these conditions. It is apparent that the Schlieren optical system described in the last section is ideally suited for measuring the displacement of this boundary with time. Since the velocity of the boundary and that of the particles are the same, the sedimentation coefficient is readily measured. 

The particle can be assumed to be spherical, in which case M/N can be replaced by (4/3)ttR P2, and f by 671770R- In this case the radius can be evaluated from the sedimentation coefficient s = 2R (p2 - p)/9t7o. Then, working in reverse, we can evaluate M and f from R. These quantities are called, respectively, the mass, friction factor, and radius of an equivalent sphere, a hypothetical spherical particle which settles at the same rate as the actual molecule. 

Mandelkern and Floryt have assembled the sedimentation coefficients and intrinsic viscosities for polymers of various molecular weights. As shown... 

Determine the sedimentation coefficient of this enzyme and, from this, its... 

Centrifugation methods separate macromolecules on the basis of their characteristic densities. Particles tend to fail through a solution if the density of the solution is less than the density of the particle. The velocity of the particle through the medium is proportional to the difference in density between the particle and the solution. The tendency of any particle to move through a solution under centrifugal force is given by the sedimentation coefficient, S ... 

Paudjojo was able to show by ultracentrifuge measurements that there is a strong specific interaction between (Lys) and CIO4, however no measurable one between (Lys)n and SO According to her results, the sedimentation coefficient... 

Properties of Latia luciferase and the purple protein. The absorption spectra of purified Latia luciferase and the purple protein are shown in Fig. 6.1.4. The sedimentation coefficient (sjo) of the... 

Fig. 3 Concentration dependence of the sedimentation coefficient for wheat amylopectin. The data have been fitted to Eq. 5 (see text) yielding s = (120d= 10)S, = (170=b60)ml/g...

Although only approximate analytical solutions to this partial differential equation have been available for x(s,D,r,t), accurate numerical solutions are now possible using finite element methods first introduced by Claverie and coworkers [46] and recently generalized to permit greater efficiency and stabihty [42,43] the algorithm SEDFIT [47] employs this procedure for obtaining the sedimentation coefficient distribution. 

The sedimentation coefficient s°, or its normalized form 5 0 w function of the conformation and flexibility of a macromolecule (via its translational frictional property) and its mass. So if we are going to obtain conformation and flexibility information we need to know the molecular weight (molar mass)... 

It is possible to get molecular weight from the sedimentation coefficient if we assiune a conformation or if we combine with other measurements, namely the translational diffusion coefficient via the Svedberg equation [50]... 

The sedimentation coefficient provides a useful indicator of polysaccharide conformation and flexibility in solution, particiflarly if the dependence of on Mw is known [62]. There are two levels of approach (i) a general level in which we are delineating between overall conformation types (coil, rod, sphere) (ii) a more detailed representation where we are trying to specify particle aspect ratios in the case of rigid structures or persistence lengths for linear, flexible structures. 

The relation finking the sedimentation coefficient with the molecular weight for a homologous polymer series given above is (see [61, 111]) ... 

Another scaling relation exists between the sedimentation coefficient and ks [see [10]]... 

For a cylindrical rod an expression also exists for the sedimentation coefficient [116] ... 

The sedimentation coefficient for wormlike chains was first worked out by Hearst and Stockmayer [123], later improved by Yamakawa and Fujii [124] to give this expression for s ... 

The reactants are then mixed in various proportions, and the sedimentation ratio (scompiex/smucin)—the ratio of the sedimentation coefficient of the complex to that of the pure mucin itself—is used as the measure for mucoad-hesion. The ultra-violet absorption optics on the XL-A or XL-1 ultracentrifuge have been used as the main optical detection system. Although the polysaccharide is generally invisible in the near UV ( 280 nm), at the concentrations normally employed the mucin—in uncomplexed and complexed form—is detectable. 

Ni is Avogadro s number, / the particle friction coefficient, u the velocity and v the partial specific volume of the solute [79,80]. Inertial forces are negligible and the balancing of the above forces yields the sedimentation coefficient ... 

A nice example for the utilization of scaling laws in sedimentation velocity runs with the analytical ultracentrifuge has been published by Machtle and Borger [78]. For the polyelectrolyte sodium polystyrene sulfonate (NaPSS) in 0.5 molar NaCl solution they found a scaling law for the sedimentation coefficient at... 

S] denotes the Svedberg unit (10 13s). Once such a scaling law is available, it can be used in conjunction with a rapid measurement of the sedimentation coefficient... 

It is convenient to classify particles by their rate of sedimentation per unit centrifugal field, a parameter known as the sedimentation coefficient (s), which has units of seconds. A Svedberg unit (S) is defined as a sedimentation coefficient of 1 X 10 13 seconds. 

The sedimentation coefficient may be determined by measuring the velocity of the particle at a fixed centrifuge speed (o>, in radians per second) and, from a series of observations, plotting the logarithm of the distance moved (x) against the time taken in seconds (t). The relationship is expressed by the equation ... 

Neither Fj nor F2 alone gave the characteristic fluorescence of fa and nicked fa in the presence of L-serine and pyridoxal phosphate. However, titration of a fixed amount of F2 with F2 gave rise to a fluorescence intensity 80-90% that of nicked fa at a stoichiometric ratio of Ft to F2. Moreover, both the excitation and emission spectra of the stoichiometric mixture were the same as for nicked fa. In addition, the same specific quenching of this fluorescence was shown in recombined Fj and F2 as in nicked fa. Further, the dissociation constants for L-serine and for indole were determined to be the same within experimental error for recombined Fj and F2, as for nicked fa. No significant differences were found between nicked fa and reconstituted Fj F2 in the intrinsic fluorescence of the aromatic residues, or in the sedimentation coefficients or the 200-250 nm CD spectra. From the foregoing independent lines of evidence, F2 and F2 combine to produce a structure very similar to that of nicked fa. 

The CONSULTATION function is run by using the mouse to select the text "CONSULTATION" from the computer screen. The first question of the dialogue, "Please enter the class of your sample of interest", appears on the screen. The pop-up menu lists the sample types to chose from. The investigator then uses the mouse to select the appropriate response from the pop-up menu. This question and answer procedure continues until SpinPro has enough information, typically 10 to 15 questions, from which to infer all of the relevant parameters. The dialogue is directed by SpinPro in response to answers to previous questions. Thus, if the sample is a protein, SpinPro requests the sedimentation coefficient if the sample is a nucleic acid, SpinPro requests the type of nucleic acid. At the conclusion of the dialogue, the reports are written to the disk. Using the pop-up menu, the reports can be read or saved. 

Figure 1.7 Structure of a ribosome. It is composed of two subunits the large 60S subunit has a mass of 2800 kDa and is composed of three RNA molecules and about 50 protein molecules. The smaller AOS subunit contains one RNA molecule plus around 30 protein molecules and has an aggregate mass of 1400 kDa. ( S is an abbreviabon for a Svedberg, the unit of the sedimentation coefficient. This is measured in an analybcal ultracentrifuge and is related to, but not simply proporbonal to, molecular mass.)...

Fig. 11. Effects of histone acetylation on the folding and stability of the nucleosome core particle. A. NaCl dependence of the sedimentation coefficient (s2o,w) of the nucleosome core particles with different extent of acetylation soo D] [379]. B. Dose-response curves obtained with hypo- ( ) and hyperacetylated...

Fig. 14. Effects of histone H2A ubiquitination on the folding and solubility of chromatin [221]. A. Magnesium chloride dependence of the sedimentation coefficient (S2o,w) of 208-12 nucleosome arrays. Sedimentation coefficients at a given magnesium chloride concentration are plotted relative...

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